The circle has center O, the length of arc ADC is 5π, and x = 100. What is the length of arc ABC?

Explanation

Choice B is correct. To find the length of arc ABC, first determine the measure of the central angle that subtends it. The angle for arc ADC is 100°, so the angle for arc ABC is 360° − 100° = 260°. The ratio of the arc lengths is equal to the ratio of their central angles: s/5π = 260/100. Simplifying 260/100 gives 13/5. Therefore, s/5π = 13/5, leading to s = 13π when both sides are multiplied by 5π.Option A is incorrect because 9π is less than half the circle's circumference. Option C is incorrect because 18π is the total circumference. Option D is incorrect because it represents only half of the arc ABC's length.